This study is designed 1) to evaluate the efficacy of MK-0966 25 mg compared to placebo for the prevention of Alzheimer's disease in patients with Mild Cognitive Impairment and 2) to evaluate the overall safety and tolerability of MK-0966 25 mg compared to placebo in patients with Mild Cognitive Impairment. This is a two year placebo-controlled, parallel-groups, double-blind, multicenter study (with in-house blinding), to evaluate the effects of MK-0966 25mg on the prevention of Alzheimer's disease and cognitive decline in approximately 1300 patients > and = to 65 years of age with Mild Cognitive Impairment. After completing the screening visit, all patients who qualify for the study will be randomized to placebo, or 25 mg MK-0966 given orally once a day for 20 months. The primary data analysis will compare the cumulative incidence of clinical AD between MK-0966 25 mg and placebo groups using the appropriate survival methods such as Cox proportional regressions. Safety will be evaluated by tabulation of adverse experiences and laboratory abnormalities.